As we approach the first efficacy trial of a T-cell vaccine for HIV disease, the problem of escape from immune control becomes increasingly important. A T-cell vaccine will probably not prevent infection; rather, it is hoped, the vaccine will ameliorate disease in patients, and decrease transmission in populations, by lowering viral burdens after infection. We have known of the possibility of escape from immune-control by mutation since the early 1990s, but the contributions of immune pressure and viral reproduction remain obscure^ Moreover, the maturity of mathematical modeling resembles that from the same period - when unrealistic or qualitative models led to failures to predict escape from antiviral drugs. In this Project, we will combine new information about the biology of HIV and the dynamics of the immune system, and new mathematical and statistical methodology, in order to make better predictions about escape from immune-control. We will derive new theoretical approaches to evaluating the probability of escape and improve techniques for simulating from, and estimating parameters in, realistic, quantitative models of cellular immune-system and viral dynamics. We will propose experimental protocols, to be conducted in parallel with vaccine trials, to measure the immune- and viral-parameters relevant to escape. These theoretical models and experimental protocols should aid in understanding the outcome of a T-cell vaccine trial and in formulating better candidate vaccines.